Mental Math
Lessons in this chapter
About Mental Math
Mental Math is a chapter of shortcuts, and the shortcuts are the point. These are the strategies that let a 1st grader stop counting one by one.
Add and Subtract 1 from a Number is the smallest one and the most used. Adding one is just the next counting word, so it should never need working out, and recognizing that frees a child from treating every sum as a fresh problem.
Work with Doubles of Numbers gives kids a set of anchor facts. Once 6 + 6 is known, 6 + 7 is one more and 6 + 5 is one less, which turns one memorized fact into three usable ones. This near-doubles strategy carries a surprising amount of 1st grade arithmetic.
Count on and Count Back formalises what most kids already do informally, with one rule attached: start from the larger number. Counting on from 8 to add 3 takes three steps, counting on from 3 to add 8 takes eight, and knowing to pick the first is a real saving.
Add up to 3 numbers to within 20 then combines the strategies, because the best way to add three numbers is usually to find the easy pair first. Spotting that 7 + 4 + 3 is really 7 + 3 and then 4 is exactly the flexible thinking the chapter is building.
Four lessons, four worksheets, all worked in the page. Work with Doubles of Numbers, Count on and Count Back and Add up to 3 numbers to within 20 set 1st graders math problems that are much quicker with a strategy than without one, which is the whole point of the chapter. They are free and scored as you go, so a child can see whether the shortcut actually saved them anything.
Frequently asked questions
Four lessons. Add and Subtract 1 from a Number comes first, then Work with Doubles of Numbers, which is the strategy that gets used most, then Count on and Count Back, and finally Add up to 3 numbers to within 20, where the trick is to find the easy pair first. These are the strategies named in Operations and Algebraic Thinking (1.OA).
Working an answer out in your head using a strategy rather than counting one by one. The four here are adding and subtracting 1, using doubles, counting on and back, and finding easy pairs when adding three numbers.
Facts like 4 + 4 and 7 + 7. They are easier to remember than other facts, and once a child knows one, near-doubles follow: 7 + 8 is just 7 + 7 and one more.
Starting at one number and counting forward by the other instead of counting everything from one. The rule worth teaching is to start from the larger number, so 3 + 9 is counted as nine, ten, eleven, twelve.
Because it forces flexibility. The fast route is to spot the pair that makes ten or a double first, which means a child has to look at all three numbers before starting rather than working strictly left to right.
Not by instruction. These strategies are what replaces fingers, and they replace them because they are faster, not because a child was told to stop.